Re: Help with proof, Given 0<n<m, show that there exists some t, n≤t<m, so that m-n d

The goal is to prove that t exists. We have not found it yet until the end of the proof. So in my hint I did mean starting with finding n mod (m - n). If it is 0, then t = n; if it is 1, then t = m - 1; if it is some other number between 2 and m - n - 1, then t is between n + 1 and m - 2. In fact, it is not hard to see that t = m - k where k can be easily found from n mod (m - n) (provided the last remainder is nonzero).